A finite difference approximation in which some terms producing time change are specified at an earlier time level. The approximation (fⁿ + 1 − fⁿ − 1)/2Δt = g(fⁿ + 1) + h(fⁿ) (where superscript n denotes a point in time, separated by step Δt from the prior (n − 1) and subsequent (n + 1) discrete time level) is an example of a semi-implicit approximation to df/dt = g(f) + h(f). Semi-implicit approximations may increase computational efficiency when g produces relatively higher frequencies or more rapid time changes in f than does h. See implicit time difference.